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Equation 28 · Part 4 · Why Cost and Latency Belong in the Evaluation Score, Not a Footnote

Symbol L_parallel

Lsequential(k)≈k lˉ,Lparallel(k)≈lˉ+ϵ(k),L_{\text{sequential}}(k) \approx k\,\bar{l}, \qquad L_{\text{parallel}}(k) \approx \bar{l} + \epsilon(k),
LparallelL_{\text{parallel}}

What this part means

LpL_parallel is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

LpL_parallel is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Start with how an agent handles its own failures. Suppose a task is retried up to k times under two different execution policies: sequential retry, where each attempt waits for the previous one to finish before starting, and parallel sampling, where all k attempts run concurrently and the first success is taken. Cost is roughly indifferent to which policy was used — the compute consumed scales with the number of attempts made, C(k) ≈\approx kcˉ\bar{c} , regardless of whether they ran one after another or all at once. Latency is not indifferent at all: Lsequential(k)≈k lˉ,Lparallel(k)≈lˉ+ϵ(k)L_{\text{sequential}}(k) \approx k\,\bar{l}, \qquad L_{\text{parallel}}(k) \approx \bar{l} + \epsilon(k). where ϵ(k)\epsilon(k) is a small scheduling and aggregation overhead that grows slowly with k . Two evaluations that both report…

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